Understanding the International Elasticity Puzzle

Follow @yilmazkuday

Understanding the International Elasticity Puzzle

One sentence summary: The macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the corresponding elasticity of substitution across products of foreign source countries.

The corresponding paper by Hakan Yilmazkuday has been published at Journal of Macroeconomics.

The working paper version is available here.

 
Abstract

International trade studies have higher macro elasticity measures compared to international finance studies, which has evoked mixed policy implications regarding the effects of a change in trade costs versus exchange rates on welfare measures. This so-called international elasticity puzzle is investigated in this paper by drawing attention to the alternative strategies that the two literatures use for the aggregation of foreign products in consumer utility functions. Using the implications of having a finite number of foreign countries in nested CES frameworks that are consistent with the two literatures, the discrepancy between the elasticity measures is explained by showing theoretically and confirming empirically that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the corresponding elasticity of substitution across products of foreign source countries.

Non-technical Summary

International trade studies have higher macro elasticity measures compared to international finance studies. Since price movements due to policy changes are converted into welfare adjustments through these elasticities, this observation evokes mixed policy implications regarding the effects of trade costs in international trade versus the effects of exchange rates in international finance. Due to these mixed implications on welfare, this observation is called the international elasticity puzzle.

In the literature, international finance studies mostly have a macro elasticity value of about 1.5, while international trade studies mostly have a macro elasticity value of about 5. It is implied that if we directly employ these numbers in a policy analysis, say, in order to investigate the effects of a foreign price change due to tariffs or exchange rates, international trade studies imply quantity changes that are at least three times the international finance studies.

This paper attempts to understand the international elasticity puzzle by drawing attention to the alternative strategies the two literatures have for the aggregation of foreign products in consumer utility functions. In particular, while the majority of international finance models include a unique foreign country (in their two-country frameworks) in order to have an understanding of the macroeconomic developments in the home country, the majority of international trade models include multiple foreign countries in order to investigate the bilateral trade patterns of the home country. Since having alternative numbers of foreign countries is reflected as alternative macro elasticity measures between the two literatures in a nested constant elasticity of substitution (CES) framework, as shown in this paper, the international elasticity puzzle can be understood by paying attention to the alternative ways that foreign products are aggregated in the two literatures.

Regarding the details, when a finite number of goods and foreign countries is considered in nested CES frameworks that are consistent with both literatures, this paper finds alternative expressions for the price elasticity of demand as a function of the macro elasticity measures in the two literatures. In order to investigate the conditions under which the two literatures have the very same policy implications (e.g., regarding changes in trade costs versus exchange rates), this paper equalizes the price elasticity measures between the two literatures. This strategy results in an expression that connects the alternative macro elasticity measures in the two literatures, where good-level details are cancelled out during the equalization of the price elasticity measures. In particular, it is theoretically shown that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the elasticity of substitution across products of different foreign source countries, where the weight is shown to depend on the number of foreign countries and home expenditure shares. Therefore, the alternative strategies in the two literatures for the aggregation of foreign products are reflected as alternative macro elasticity measures between the two literatures.

The implications of equalizing the price elasticity of demand measures between the two literatures are also tested empirically. Since this investigation requires data on both domestic and foreign trade, it cannot be achieved by using any international trade data set, where domestic trade data are not recorded. As an alternative, this paper uses the available trade data within the U.S. by considering interstate trade as foreign trade and intrastate trade as domestic trade. The results based on the estimation of macro elasticity measures in both literatures confirm the theoretical solution provided in this paper that the macro elasticity in international trade is a weighted average of the macro elasticity in international finance and the elasticity of substitution across products of different foreign sources. Therefore, the discrepancy between the macro elasticity measures in the two literatures can in fact be understood by paying attention to the alternative ways that foreign products are aggregated in the two literatures.

The corresponding paper by HakanYilmazkuday is available at Journal of Macroeconomics.

Redistributive Effects of Gasoline Prices

Follow @yilmazkuday

Redistributive Effects of Gasoline Prices

One sentence summary: There are significant redistributive effects of gasoline price changes among U.S. consumers, where the main determinant is shown to be the consumer income.

The corresponding paper by Demet Yilmazkuday and Hakan Yilmazkuday has been accepted for publication at Networks and Spatial Economics.

Free access to the published paper is available at https://rdcu.be/bfNqu 

The working paper version is available here.

Abstract

Consumers face significantly different gasoline prices across gas stations. Using gasoline price data obtained from 98,753 gas stations within the U.S., it is shown that such differences can be explained by a model utilizing the gasoline demand of consumers depending on their income and commuting distance/time, where the pricing strategies of both gas stations and refiners are taken into account. The corresponding welfare analysis shows that there are significant redistributive effects of gasoline price changes among consumers where the main determinant is shown to be the consumer income; e.g., welfare costs of an increase in gasoline prices are found to be higher for lower income consumers.

Non-technical Summary
Gasoline prices have significant effects on an economy, because higher energy prices can slow economic growth and affect individual welfare in many ways. As one example, gasoline prices have increased before any historical economic downturn in the U.S. As another example, consider the survey reported by Bankrate.com in May 2012, which depicts that, from the end of December 2011 through mid-April 2012, the price of regular gas rose from a national average of $3.30 per gallon to $3.94 (an increase about 19%), and, as a result, 59% of consumers cut back on nonessential spending on things such as vacations and dining out, only because of gasoline price changes. These macroeconomic examples provide an average picture of the gasoline price effects, but is the magnitude of these effects the same across consumers? The answer to this question is essential to understand the redistributive effects of gasoline prices, especially when gasoline prices differ across consumers.

Consider the following figure where each circle represents the location of a gas station. The colors of the circles represent the prices in U.S. dollars per gallon. Price intervals represent the intervals corresponding to the first, second, third, fourth and fifth 20th percentile of average of daily gasoline prices obtained from 98,753 gas stations between September 8th and September 14th, 2014. As is evident, while the gasoline prices are more expensive in the Northeast and the West (including Alaska and Hawaii), they are relatively cheaper in the Southeast.

To better understand the magnitude of gasoline price differences across consumers, consider a typical day (of September 14th, 2014) when the retail-level gasoline price difference between any two gas stations within the U.S. was as high as $2.28 per gallon of regular gas. If you think that this price dispersion was due to differences in state-taxes per gallon, which ranged between 42.75 cents (for New York) and 8 cents (for Georgia) in 2014, you are only partially right, because, for a typical day (of September 14th, 2014), the price difference between any two gas stations within any given state of the U.S. was as high as $1.68 (for the state of Massachusetts) followed by $0.99 (for the state of New York). Therefore, a detailed analysis is required to understand gasoline price dispersion at the gas-station level, which is the key to the investigation of the redistributive effects of gasoline price changes.

This paper achieves such an investigation by modeling the gasoline consumption of individuals and the pricing strategy of gas stations and refiners. The optimization in the model results in the gasoline demand of consumers depending on their income and commuting requirements as well as the price of gasoline. Gas stations take this demand into consideration while maximizing their profits, which results in a linear gasoline price expression due to having Leontief production functions. Refiners take into account the demand coming from gas stations to maximize their own profits. When the behavior of all agents in the model are combined, a final expression for gasoline prices is obtained at the gas station level, which depends on the income and commuting behavior of consumers as well as refiner-related costs.

Using data on gas-station level gasoline prices, zip-code level income and zip-code level commuting within the U.S., the implications of the model are estimated. The results show that most of the variation of gasoline prices (across gas stations) is explained by the proposed model. As a supplementary result, the average (across gas stations) markup per gallon is estimated about 16 cents, which is consistent with the surveys achieved by independent organizations.

After showing that the implications of the proposed model are consistent with gasoline price data, together with other supplementary data, we move to the welfare analysis to investigate the redistributive effects of gasoline price changes across consumers within the U.S.. The implications of the model combined with the results coming from the empirical investigation suggest that 1 percent of an increase in gasoline prices can lead to a reduction in consumer utility ranging between 0.08 percent and 2.76 percent (with an average of 0.82 percent) within the U.S.. Therefore, there are in fact significant redistributive effects of gasoline price changes. When the sources of these redistributive effects are further investigated, it is shown that consumer income is the main determinant; i.e., welfare costs related to a gasoline price increase are higher for lower-income consumers. It is implied that, in order to minimize the redistributive welfare effects of gasoline price changes, special policies should be conducted for lower-income consumers, especially when gasoline prices increase significantly.

Although gasoline prices can be affected by income, commuting distance/time, oil prices, and refiner costs according to the proposed model, they can also be affected by local or national taxes that have not been modeled here (nevertheless, they have been controlled for in the empirical investigation). Therefore, a change in any of these variables would change gasoline prices, and, thus, any policy conducted on such variables would result in redistributive welfare effects among consumers according to the analysis, above. Accordingly, one policy suggestion would be to provide gasoline tax cuts for neighborhoods with lower-income consumers. Providing tax reimbursements for lower-income consumers depending on their gasoline consumption and/or the gasoline (or oil) price changes over the preceding year can also be considered. Another one would be to promote/subsidize fuel-efficient cars for lower-income consumers that would effectively reduce the share of gasoline in their expenditure. Even though the formal investigation of such suggestions is out of the scope of this paper, future research can focus on the public policy implications of a more local analysis based on the insights of this study.

The working paper version is available here.

Unequal Exchange Rate Pass-Through across Income Groups

Follow @yilmazkuday

Unequal Exchange Rate Pass-Through across Income Groups

One sentence summary: There is evidence for redistributive effects of an exchange rate shock across income groups.

The corresponding paper by Hakan Yilmazkuday has been accepted for publication at Macroeconomic Dynamics. 

The working paper version is available here.

Abstract

Exchange rate pass-through (ERPT) into prices and into income loss are shown to be enough to calculate ERPT into welfare loss by using implications of a simple model. These ERPT measures are estimated at the good level by using a unique micro-price data set from Turkey, and they are combined with income-group specific expenditure shares at the good level to obtain aggregate-level ERPT measures for alternative income groups. An exchange rate shock resulting in a real depreciation of 1% is shown to decrease welfare by about 0.80% for the average-income consumer, while this estimate ranges between 0.73% and 0.83% for consumers in the lowest and highest income quintiles, respectively, suggesting evidence for redistributive effects of an exchange rate shock. Using micro prices has further resulted in showing that traded, nondurable, flexible-price, or income-elastic goods contribute more to ERPT into welfare loss for the average-income consumer, suggesting important policy implications for filtering out the noise in the measurement of aggregate-level prices.

Non-technical Summary

Open economies are subject to international shocks that are mostly reflected as movements in their exchange rates. The effects of such movements, the so-called exchange rate pass-through (ERPT) measures, highly depend on the extent of expenditure switching between domestic and foreign goods, which may take time to observe due to price stickiness. Especially when exchange rate movements are not fully reflected in prices (i.e., incomplete ERPT into prices), there are significant welfare effects due to price setting in the currency of consumers versus producers that should be taken into account by policy makers. Therefore, it is not only important to understand ERPT into prices but also into quantities and thus welfare, both in the short and long-run. This paper follows such an approach by estimating ERPT into prices, income and welfare for alternative horizons.

Although there is a large body of literature investigating/estimating ERPT measures into prices, the existing evidence on ERPT is mostly at the aggregate level, suppressing disaggregated-level details such as income redistributive effects of exchange rate movements among consumers. Despite several studies in the literature that have proposed such income redistributive effects in their theoretical frameworks, to our knowledge, there is no corresponding empirical evidence. The lack of empirical evidence is mostly because aggregate-level prices (e.g., consumer price index) are published only for the average-income consumer, while the investigation of redistributive effects requires the knowledge of prices faced by alternative income groups. This paper proposes a solution to this problem by using a good-level investigation. In particular, with the knowledge of the set of goods consumed by each income group, we use the corresponding micro prices to estimate ERPT measures at the good level, which are further combined with the expenditure shares of goods for each income group to estimate the aggregate welfare effects.

Estimating ERPT measures at the good level (as in this paper) is also useful for avoiding any aggregation bias, since estimations at the aggregate level suppress several micro-level details. These include micro-level distortions such as price stickiness, tradability of goods, degree of competition reflected in markups, transportation costs in different sectors, or the quality of goods. These micro-level details not only are important to understand the economic intuition behind ERPT into good-level prices but also can be used to identify the goods/sectors responsible for the effects of exchange rate movements at the aggregate level. By using a good-level approach, this paper not only considers these micro-level details by construction but also achieves further decomposition analyses showing the contribution of each good category to ERPT measures for each income group.

Finding the goods/sectors that are responsible for ERPT measures has important monetary policy implications as well, because, understanding changes in micro prices can offer more relevant information about the nature of inflation in countries such as Turkey, where good-level prices change more frequently compared to other countries. In particular, to have a healthy measure of inflation that can be used for optimal policy making, the noise in aggregate-level prices should be filtered out by using measures such as the trend or core inflation, and using disaggregate-level price data to determine the responsible goods/sectors (as in this paper) is one way to do it as suggested by several studies in the literature. These measures are also useful to increase the effectiveness of communicating monetary policy actions in an environment of frequently changing prices.

Regarding the estimation methodology, several empirical studies in the literature have considered single-equation frameworks that result in endogeneity bias. Also considering our discussion on micro-level details above, it is implied that an empirical investigation based on a system of equations at the good level is necessary to avoid both aggregation and endogeneity biases in the estimation of ERPT measures. This paper achieves such an unbiased estimation of ERPT by using a structural VAR model at the good level, where ERPT ratios are considered for the measurement of ERPT. Specifically, ERPT into prices (income) is measured as the cumulative response of prices (income) divided by the cumulative response of exchange rates, both following an exchange rate shock. Such an approach followed at the good level effectively addresses concerns related to both aggregation and endogeneity biases. Micro-price data, good-level expenditure shares for alternative income groups, together with data on income and exchange rates, are used from Turkey over the monthly period between 2004m1-2018m12. Once ERPT into prices and income are estimated, by using the implications of a simple model introduced in this paper, ERPT into welfare is calculated as ERPT into income minus ERPT into prices.

The results for the average-income consumer suggest that an exchange rate shock resulting in a 1% depreciation of the currency increases the aggregate price index by about 0.45%, reduces income by about 0.34%, and reduces welfare by about 0.80%. When the same investigation is achieved across alternative income groups, the welfare loss ranges between 0.73% and 0.83% for consumers in the first and last income quintiles, respectively, suggesting redistributive effects of an exchange rate change among consumers.

The good-level investigation in this paper also allows for the decomposition of this aggregate-level result into the contribution of each good category to the welfare of alternative income groups. In particular, among good categories, those that are traded, nondurable, flexible-price, or income-elastic contribute more to ERPT into welfare for the average-income consumer, and the contribution of durable and income-elastic goods gets higher with consumer income.

Among sectors, "Food and Non-Alcoholic Beverages" followed by "Communications" and "Transport" contribute the most to ERPT into welfare for the average-income consumer, although this decomposition differs significantly across income groups. Specifically, ERPT into welfare is mostly through "Food and Non-Alcoholic Beverages" and "Housing, Water, Electricity, Gas and Other Fuels" for the lowest-income consumers, while it is mostly through "Transport" and "Communications" for the highest-income consumers. Due to their higher contribution to ERPT measures, it is implied that these sectors should be paid more attention while measuring the trend/core inflation and thus conducting policy.

Unequal Welfare Gains from Trade across Countries: The Role of Aggregation and Income Elasticities

Follow @yilmazkuday

Unequal Welfare Gains from Trade across Countries: The Role of Aggregation and Income Elasticities

One sentence summary: Equal percentage changes in home expenditure shares result in unequal gains across countries depending on their elasticity measures.

 

The corresponding academic paper by Hakan Yilmazkuday has been accepted for publication at International Economic Journal.

The working paper version is available here.

Abstract

Sectoral heterogeneity has been shown to affect country-level welfare gains from trade that can be calculated by sector-specific trade elasticities and home expenditure shares. However, empirical analyses of multi-sector models are restricted to a limited number of countries and sectors, mostly due to the lack of data on sector-specific home expenditure shares. This paper first proposes a solution to this limitation by changing the way that foreign products are aggregated at the destination country, where "unbiased" multi-sector welfare gains can be captured by using country-specific trade elasticity measures. Second, the restrictive assumption of unitary importer-income elasticity is relaxed, and it is shown that the trade elasticity in the calculation of welfare gains is replaced by the newly-introduced welfare elasticity, a function of trade and income elasticities. Empirical evidence suggests that equal percentage changes in home expenditure shares result in unequal gains across countries depending on their elasticity measures.

Non-technical Summary
Welfare gains from trade (measured as costs of autarky) can be captured by two key parameters, namely the trade elasticity and home expenditure share in a one-sector environment for a variety of models. Nevertheless, such a convenient calculation may be biased, since one-sector models ignore the interaction among sectors. It is implied that sectoral heterogeneity is accepted as a key ingredient in welfare calculations. However, when the one-sector environment is extended to a multi-sector one, due to the way that sectors are aggregated at the destination country (i.e., an upper-tier aggregation of utility across sectors), the two key parameters are required at the sector level in order to calculate welfare gains from trade; moreover, an additional/third parameter is required at the sector-level to capture sector shares. Although the trade elasticity can be estimated for pretty much any sector and any country by using the corresponding trade and price/tariff data, sector shares and sector-specific home expenditure shares are available only for certain aggregation of sectors in certain countries. Accordingly, in order to calculate welfare gains in a multi-sector environment, several studies focusing on the estimation of both parameters (at the sectoral level) have been restricted to a limited number of countries and a limited number of sectors. Moreover, when the number of countries is limited, the estimated elasticity parameters (especially those that are common across countries) simply cannot represent global trade patterns, which would lead into biased welfare calculations.

In order to address these issues, this paper changes the way that foreign products are aggregated at the destination country so that the trade elasticity and aggregate home expenditure share are enough to calculate welfare gains from trade in a multi-sector framework. This is achieved for each destination country by having an upper-tier aggregation across source countries, and a middle-tier aggregation across sectors. To ensure that the sectoral heterogeneity will still be captured after this change in the order of aggregation, we borrow the concept of "unbiased" welfare gains from the literature and consider country-specific trade elasticity measures. When this proposal is empirically tested, it is shown by the following figure that country-specific trade elasticity measures can in fact be used to obtain "unbiased" multi-sector welfare gains.

Another bias in the calculation of welfare gains may arise due to restrictive assumption of unitary importer-income elasticity. In particular, studies in the literature have shown due to source-specific importer-income elasticity measures that higher importer income results in unequal welfare gains across source countries depending on the average type of product (inferior or luxury) exported by the source country. It is implied that measuring "unbiased" welfare gains also requires the consideration of source-specific importer-income elasticity measures.

Based on this motivation, this paper considers source-specific importer-income elasticity measures by using implicitly additively separable nonhomothetic constant elasticity of substitution (CES) preferences across source countries at the upper-tier aggregation of destination utility. Such an approach is useful to separately capture the source-country-specific importer-income effects in the utility function of destination countries, without giving away the standard features of having CES preferences, so that one can easily distinguish between income and substitution effects.

Based on the discussion so far, this paper considers an upper-tier aggregation across source countries by using implicitly additively separable nonhomothetic CES preferences, a middle-tier aggregation across sectors by a Cobb-Douglas function, and a lower tier aggregation across firm-level goods by CES preferences. The implications of the model regarding trade is estimated at the bilateral country level by using UN Comtrade data between 1995-2015. Since the lower tier aggregation of individual utility is achieved across firm-level goods in the model, firm-level productivity differences are carefully connected to the data on unit prices and the corresponding estimation; therefore, although firm-level data are not utilized, firm-level productivity differences are still taken into account at the aggregated level, without making any assumptions on their distribution. Due to the tiers of aggregation introduced so far, this corresponds to having a weighted average of sectoral log unit prices (measured at the six-digit Harmonized System in UN Comtrade) in the bilateral aggregate trade estimation, where the weights are simply the expenditure weights of sectors. Nevertheless, since firm-level productivity measures are carried over to the bilateral aggregate trade estimation as residuals, aggregated log unit prices become endogenous. By using the implications of the model, bilateral trade costs measured by standard gravity variables are shown to be potential instruments for aggregated unit prices in a Two-Stage Least Squares (TSLS) estimation. In this bilateral aggregate trade estimation, the coefficient in front of aggregated unit prices represents the destination-specific trade elasticity (i.e., one minus the elasticity of substitution), while the coefficient in front of log real total consumption (due to having non-unitary income elasticity) represents the source-specific income elasticity; these estimates are further used to construct country-specific welfare elasticity estimates.

The corresponding welfare elasticity estimates have an average value of -5.40 across countries with a range between -7.33 and -2.99. In order to show the contribution of this paper in a clear way, the obtained welfare elasticity estimates are further compared to the common (across countries) trade elasticity estimate of about -4.95 that is obtained by the very same data set. With respect to the welfare gains obtained by the welfare elasticity, the welfare gains obtained by the common trade elasticity are underestimated by up to about 14% for highly-trading or high-income countries such as Ireland, Switzerland, and Germany, while they are overestimated by up to about 9% for less-trading or low-income countries such as Congo, Aruba and Guyana. When we search for a systematic explanation for the heterogeneity of these biases across countries by using the implications of our model, we show that it is not only connected to per capita income of countries but also connected to the total trade of source countries. This heterogeneity across countries is also reflected in the calculation of global welfare gains, where they range between 6.70% and 8.38% when heterogeneity is ignored and considered, respectively. 

 

 

The corresponding academic paper by Hakan Yilmazkuday has been accepted for publication at International Economic Journal.

The working paper version is available here.